Reach Mt Fuji Fujinomiya 5th Station July 10?

I planned my trip so that I will be able to climb the Fujinomiya trail on the opening day, which I have confirmed is July 10th. Despite this being the opening day, according to the bus timetables, (https://www.japan-guide.com/bus/fuji.html), the climbing season bus schedule doesn't begin until July 12th. Unfortunately this means that there is seemingly only 1 morning shuttle to Fujinomiya 5th station on July 10th, which leaves shin-fuji station at 8:25am. This leaves me with the following questions:

Can tickets for this shuttle be purchased online?
If not, how early should I arrive at Shin-Fuji station, and how easy will it be to tell where to wait?
Are there other means of getting to the 5th station besides those on the shuttle bus timetable on this website?

I am planning to come down on the Yoshida side so really only getting up is the issue, but I do wonder:

Will I have any trouble getting a shuttle to Fujiyoshida (or whichever city most shuttles go to) without reservations when I get to the bottom?
The following day, what would be the best way to get from Fujiyoshida to Tokyo with a JR pass?

Any insight would be greatly appreciated - thanks!